A high-speed 100 MHz strain monitor using a fiber Bragg grating, an optical filter, and a mode-locked optical fiber laser has been devised, which has a resolution of $Delta L/Lsim10^{-4}$. The strain monitor is sufficiently fast and robust for the magnetostriction measurements of magnetic materials under ultrahigh magnetic fields generated with destructive pulse magnets, where the sweep rate is in the range of 10-100 T/$mu$s. As a working example, the magnetostriction of LaCoO$_{3}$ was measured at room temperature, 115 K, and 7$sim$4.2 K up to a maximum magnetic field of 150 T. The smooth $B^{2}$ dependence and the first-order transition were observed at 115 K and 7$sim$4.2 K, respectively, reflecting the field-induced spin-state evolution.